Contact erosion initiated by clay dispersion beneath pavement layers

ABSTRACT

Dispersive failures have been reported throughout the world in the recent past. Soils, in which they occur, are vulnerable to erosion even in quiet water. The initiation of dispersive failure below the pavement layers would progress without any sign and the consequences would be more severe than other types of pavement failure. This paper describes a theoretical development of an analytical model to quantify the mass of particle loss due to dispersion failure below the pavement layers and the associated transport and deposition of the detached particles. The analytical model is validated using the experimental results for four different materials with dispersive characteristics. The model calculations are compared with the experimental results and a close correlation is found between the model-calculated and experimental results. The calculated total mass loss per unit area for the most dispersive soil is 1.90 g/cm², which is very close to the experimental result of 1.72 g/cm². The study indicates that the mass loss in the first water contact is significantly greater than those in the subsequent cycles for all the materials in the analytical and experimental results. Also, the calculated total mass loss is very close to the experimental results.

KEYWORDS:

• Soil erosion
• dispersive clay
• contact erosion
• modelling
• pavement layers

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Correction

List of Notations

$a$	=	Radius of particle transported through the pores
${\mathrm{a}}_{\mathrm{f}}$	=	Radius of the settling flocs
$A$	=	Activity of the soil
${\mathrm{A}}^{\prime }$	=	Unique constant to a particular soil
${\mathrm{A}}_{\mathrm{x}\mathrm{y}}$	=	Cross sectional area Axy
$b_c$	=	Standard deviation of the log-normal distribution of pore radius of working platform material
$B,B_1$	=	Arbitrary constant
$C\left(x,t\right)$	=	Concentration of particles
$C_p$	=	Mass concentration of primary particles
$C_g$	=	Gelling concentration needed for mud floc to form interconnected network
$C_{Na}\left(t\right)$	=	Concentration of Na+ ions at the interface at time $t$
$C_C\left(t\right)$	=	Mass concentration of eroded materials at time $t$ in the working platform layer
$d_{mf}$	=	Mean diameter of the filter particles based on number of particles
$d_{15C}$	=	Particle size in working platform material for which 15% by weight of particles are smaller
$d_{85E}$	=	Particle size in embankment material for which 85% by weight of particles are smaller
$D_f$	=	Diameter of the floc
$d_0$	=	Diameter of the primary particle
$D$	=	Dispersion coefficient
${\mathrm{D}}_{\mathrm{N}\mathrm{a}}$	=	Diffusion coefficient of Na+ ions
e	=	Void ratio of the working platform
E	=	Erosion rate
$F$	=	Fractal dimension of flocs
$g$	=	Gravitational acceleration
$h_c$	=	Height of coarse aggregate layer
$I_p$	=	Plastic index
$I_s$	=	Ionic strength estimated based on the equivalent atomic weight of major monovalent and divalent cations present in the soil solution
$L_a$	=	Particle travel distance
m	=	Mean of the log- normal distribution of pore radius
$m_c$	=	Mean of the log- normal distribution of pore radius of working platform material
$M$	=	Total mass of Na+ ions available to pass through the interface per unit area
$M_C$	=	Mass loss of clay particles at the interface
$M_{Tot}$	=	Mass of total particles detached at the interface
$M_{DWT}$	=	Total mass transported as a result of dragging force created by the gravitational water draw down through the coarse aggregate materials
$M_{GT}$	=	Mass of materials transported through the coarse aggregate layer under the gravitational settling
$M_{TT}$	=	Total mass of embankment material transported through the working platform layer
$M_D$	=	Mass of material deposited by physico-chemical capture within the working platform layer
$M_{Na}$	=	Mass loss of Na+ ions at the interface
$M_{PD}$	=	Mass of physically captured soil particles in the working platform layer
$N\left(t\right)$	=	Concentration of Particles captured in the working platform material by physico-chemical attraction
$r_i$	=	Pore radius
$R_i$	=	Particle radius
$R_e$	=	Reynolds No
$S$	=	Amount of particles deposited in a soil filter as a result of physico-chemical attraction
$t$	=	Time variable
$V$	=	Advective velocity
${\mathrm{V}}_{\mathrm{c}}$	=	Critical velocity for the base soil materials
$V_s$	=	Settling velocity
${\mathrm{V}}_{\mathrm{s}\mathrm{p}}$	=	Effective gravitational settling velocity of eroded floc in the pore solution of the working platform layer
${\mathrm{V}}_{\mathrm{s}\mathrm{c}}$	=	Unbounded settling velocity of flocs in the working platform
$V_{hs}$	=	Hindered settling velocity of floc
$V_{bs}$	=	Bounded settling velocity
$V_m$	=	Velocity of flow through the pores of the coarse aggregate material
$w$	=	Excess moisture content above the optimum moisture content
$x,z$	=	Space variable
$\beta$	=	Rate of change of erosion rate/erosion coefficient $\left(kg/Ns\right)$
${\beta }_e$	=	Erosion coefficient of deposited dispersive eroded materials
${\tau }_w$	=	Applied shear stress/shear stress induce by flow of water (N/m2)
${\tau }_c$	=	Critical shear stress $\left(N/m^2\right)$
$\lambda$	=	Deposition coefficient
${\lambda }_m$	=	Modified deposition coefficient
$b$	=	Standard deviation
${\xi }^{\prime }$	=	Shape factor
$\theta$	=	Lump parameter representing the effect of several inter-particle forces on deposition
$\psi$	=	Effective length of pore tubes in the direction of flow
${\theta }_i$	=	Parameter representing the ionic conditions of pore fluid
${\theta }_{id}$	=	Parameter representing the ionic conditions of pore solutions containing soils with dispersive characteristics
${\theta }_f$	=	Modified parameter representing particle attraction force on settling flocs
${\theta }_{ic}$	=	Value of ${\theta }_i$ for normal clayey soils in pure water
${\rho }_w$	=	Water density (kgm−3)
${\rho }_f$	=	Density of floc
${\rho }_p$	=	Primary particle density (kgm−3)
$\mu$	=	Dynamic viscosity of the pore water (kgm−1s−1)
${\varphi }_p$	=	Volumetric concentration of primary particles within flocs
${\varphi }_f$	=	Volumetric concentration of floc
${\mu }_m$	=	Effective viscosity
${\varsigma }^{\prime }$	=	Ratio of particle diameter to the tube diameter
$\varsigma$	=	Ratio between the diameter of floc and the mean diameter of pore openings in the coarse aggregate layer
${\zeta }_m$	=	Mass ratio of sodium to mass of particles passing 300 µm in the selected embankment fill material
${\zeta }_c$	=	Ratio of mass of sodium to mass of clay particles in the selected embankment soil
$\epsilon$	=	Pore volume ratio of embankment layer to coarse aggregate layer
δ	=	Equivalent atomic mass of ions in 100g (meq/100g) of primary soil
${\epsilon }_c$	=	Ratio of the volume of deposited materials to the pore volume of working platform layer
$\xi$	=	Modified shape factor
${\sigma }_b$	=	Parameter based on the ratio of equivalent atomic mass of Na+ ions to the average equivalent atomic weight of divalent cations in 100g of primary soil
${\sigma }_e$	=	Ratio of equivalent atomic weight of Na ions to the equivalent atomic weight of Ca2+ ions in the pore solution
$\kappa$	=	Factor representing the diffusive force applied on Na+ ions

Disclosure statement

No potential conflict of interest was reported by the author(s).